Peter Scheuer started this. In 1977 he walked into JVW's office in the Cavendish Lab and quietly asked for advice on what further material should be taught to the new intake of Radio Astronomy graduate students (that year including the hapless CRJ). JVW, wrestling with simple chi-square testing at the time, blurted out ‘They know nothing about practical statistics’. Peter left thoughtfully. A day later he returned. ‘Good news! The Management Board has decided that the students are going to have a course on practical statistics.’ Can I sit in, JVW asked innocently. ‘Better news! The Management Board has decided that you're going to teach it’.

So, for us, began the notion of practical statistics. A subject that began with gambling is not an arcane academic pursuit, but it is certainly subtle as well. It is fitting that Peter Scheuer was involved at the beginning of this (lengthy) project; his style of science exemplified both subtlety and pragmatism. We hope that we can convey something of both. If an echo of Peter's booming laugh is sometimes heard in these pages, it is because we both learned from him that a useful answer is often much easier – and certainly much more entertaining – than you at first think.

After the initial course, the material for this book grew out of various further courses, journal articles, and the abundant personal experience that results from understanding just a little of any field of knowledge that counts Gauss and Laplace amongst its originators.

There is a vast literature. Here we point to a few works which we have found useful, binning these into five types: popular, the basic text, the rigorous text, the data analysis manual, and the books of specialist interest to astronomers.

1. classic popular books have legendary titles: How to Lie with Statistics (Huff 1973), Facts from Figures (Moroney 1965), Statistics in Action (Sprent 1977) and Statistics without Tears (Rowntree 1981). They are all fun. A modern version with a twist in the title is Seeing through Statistics (Utts 1996), which entertains, serves as a statistics primer, and is almost a member of the next group.

2. come in types (a) and (b), both of which cover similar material for the first two-thirds of each book. They start with descriptive or summarizing statistics (mean, standard deviation), the distributions of these statistics, then moving to the concept of probability and hence statistical inference and hypothesis testing, including correlation of two variables. They then diverge, choosing from a menu including analysis of variance (ANOVA), regression analysis, non-parametric statistics, etc. Modern versions come in bright colours and flavours, perhaps to help presentation to undergraduates of a subject with which excitement is not always associated. The value of many such books is exceptional because of the sales they generate. They are complete with tables, ready summaries of tests and formulae inside covers or in coloured insets, and frequently arrive with CDs and floppy disks including test datasets. […]

When we make a set of measurements, it is instinct to try to correlate the observations with other results. One or more motives may be involved in this instinct: for instance we might wish (1) to check that other observers' measurements are reasonable, (2) to check that our measurements are reasonable, (3) to test a hypothesis, perhaps one for which the observations were explicitly made, or (4) in the absence of any hypothesis, any knowledge, or anything better to do with the data, to find if they are correlated with other results in the hope of discovering some new and universal truth.

4.1 The fishing trip

Take the last point first. Suppose that we have plotted something against something, on a fishing expedition of this type. There are grave dangers on this expedition, and we must ask ourselves the following questions.

This happens every year. It is Marathon morning. You have observed the maximum number of Messier Objects from your location. You ask: ‘What's next?’ You could wait until the following year and work the Messier Marathon again. Many amateur astronomers do this, and find it becomes easier each year. You can also wait until October or November and see nearly all the Messier Objects in one night (see Chapter 3). You can also go out the next night and do the Messier Marathon all over again with some variation.

Ideas for different Messier Marathons

Photographic or CCD Marathon

How about photographing or obtaining a CCD image of each object? You could image about as many objects as you can see.

Photographs for most objects would require fast film and one or two minutes exposure per photograph. Due to the way the Objects are grouped, the 110 Messier Objects would require about ninety-one photographs, if your field of view were three degrees. You can photograph through the telescope or mount the camera piggyback on a guiding scope and use a telephoto lens.

ACCD, or charged coupled device, is an ‘electronic’ camera attached to your telescope. The image is transformed into electronic impulses that are sent to your computer.

Charles Messier lived and worked during a pivotal point in visual astronomical history. He was one of the first comet hunters, discovering new comets over a span of four decades, and recording nearly every observable comet during his career.

His comet hunting resulted in an extensive knowledge of the night sky, enabling him to organize a catalog of galaxies, clusters and nebulae. This list of heavenly wonders, known as the Messier Catalogue, has become one of the most popular lists of its kind. It includes many of the brightest and best-known objects in the night sky. Yet the 110 marvels are few enough that even the beginning amateur astronomer of today can find them all, or nearly all, of them in one night.

Born on June 26, 1730, in Lorraine, France, Charles was the tenth of twelve children. His father died when he was eleven. Three years later, in early 1744, the young Charles observed the brilliant multitailed comet of 1744. A month after his eighteenth birthday, in July 1748, he observed an annular solar eclipse from his home town. In October 1751 he went to Paris in search of a new life. His skill in penmanship and drafting landed him employment as a record keeper at a small observatory at the Hotel de Cluny.

As seen from Chart 3.1, the Messier Objects are not evenly distributed throughout the sky. A large concentration of galaxies appears in the constellation Virgo, and across the border in the small constellation Coma Berenices. Another group of Objects, consisting mostly of open and globular star clusters, resides in Sagittarius. Meanwhile, a few areas in the sky contain no Messier Objects, notably near the Great Square of Pegasus, but also between Ursa Major and Gemini.

As the sun travels through the sky each year on the ecliptic (see Chart 3.1), the adjacent portions of the sky are not easily visible from the Earth because they rise and set with the sun. For example, when the sun is ‘in’ Gemini, as it is during early July, then it is located in front of the stars that form the constellation that we call Gemini. The stars of Gemini rise at the same time as the sun does. And, as even the non-astronomer notices, the sky brightens for at least an hour before sunrise, making observation of these stars increasingly difficult as dawn advances. Therefore the stars that rise shortly before Gemini are invisible as well. At the end of the day, Gemini sets with the sun.

Lists of non-stellar heavenly bodies – galaxies, clusters and nebulae–were common in Messier's time. Ptolemy compiled one of the earliest such lists in the second century AD. Tycho Brahe had published a list of six nebulae in 1601, as did Edmond Halley in 1715. Abbe Nicholas-Louis de la Caille (Lacaille) produced a tabulation of forty-two objects in the southern sky in 1755, and John Bode published seventy-five objects in 1777.

Perhaps no one was in a better position to compile such a catalog than comet hunter Charles Messier. He had both the means and a motive. Countless nights under the sky sharpened his knowledge of the location and appearance of the objects. This was augmented by his mapping skills.

Messier's main motive for assembling his Catalogue seems to be best summed up in his memoir in the journal Connaissance des Temps for 1801. In it he wrote:

Imagine yourself standing next to your telescope at evening twilight. It is late March. The sky is clear, the wind still. It is the night of the Messier Marathon. Tonight you will have the opportunity to locate and observe 110 galaxies, star clusters and nebulae cataloged 200 years ago by a French astronomer named Charles Messier. This basic list contains some of the best astronomical objects ever seen. Most amateur astronomers don't bother finding all of them in a lifetime; you are going to marathon through the whole list in one night.

You begin by working your way upward from the western horizon. After these galaxies you enter the open clusters and nebulae of the winter Milky Way. The variety of these wonders is astonishing.

Time passes quickly. You have been marathoning at a leisurely pace for nearly two hours now. Already you are examining the galaxies high in the sky near the Big Dipper. Next comes the area you have feared the most – the Virgo Galaxies. You set out on it using your trusty star chart. In twenty minutes you have picked up seventeen more Messier Objects. ‘This is easy,’ you think.

It is now 10:30 PM. You have seen sixty-six of the 110 Messier Objects.